Device and method of multi-dimensional frequency domain extrapolation of sensor data

ABSTRACT

Embodiments of a device and a frequency data extrapolator are generally described herein. The frequency data extrapolator may receive input frequency data mapped to a two-dimensional frequency grid. As an example, the input frequency data may be based on return signals received, at a sensor of the device, in response to pulsed transmissions of the sensor in a physical environment. Regions of the frequency grid may be classified as high fidelity or low fidelity. A group of basis rectangles may be determined within the high fidelity regions. A column-wise extrapolation matrix and a row-wise extrapolation matrix may be determined based on the input frequency data of the basis rectangles. The input frequency data of the high fidelity regions may be extrapolated to replace the input frequency data of the low fidelity regions.

TECHNICAL FIELD

Some embodiments pertain to radar devices. Some embodiments relate tosonar devices. Some embodiments relate to sensors, including coherentlypulsed sensors. Some embodiments relate to frequency data processing,including frequency data processing in two dimensions. Some embodimentsrelate to image processing. including image processing in two or moredimensions. Some embodiments relate to extrapolation and/orinterpolation, including extrapolation and/or interpolation in two ormore dimensions.

BACKGROUND

In some scenarios, information about a physical environment may bedetermined by a device, such as a radar device, sonar device or otherdevice. For instance, a topology of the environment, a physicalcondition of the environment, a speed or position of an element in theenvironment or other aspects may be determined. Various techniques thatutilize sensors, such as coherently pulsed sensors, may be used in somecases. As an example, the sensors may collect time data and/or frequencydata for further processing to determine various pieces of informationabout the environment. When a portion of the time data and/or frequencydata is incomplete, flawed, noisy or missing, the desired output of thedevice may be inaccurate. Accordingly, there is a general need formethods and systems to improve processing of such data in these andother scenarios.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example device in accordance with someembodiments;

FIG. 2 illustrates an example of pulsed sensor operation in accordancewith some embodiments;

FIG. 3 illustrates examples of a compressed image domain and a dispersedFourier domain in accordance with some embodiments;

FIG. 4 illustrates the operation of an example method of frequencydomain extrapolation of sensor data in accordance with some embodiments:

FIG. 5 illustrates additional examples of a compressed image domain anda dispersed Fourier domain in accordance with some embodiments;

FIG. 6 illustrates an example of a group of basis rectangles inaccordance with some embodiments;

FIG. 7 illustrates an example of determination of extrapolation matrixesin accordance with some embodiments;

FIG. 8 illustrates an example of extrapolation in accordance with someembodiments;

FIG. 9 illustrates additional examples of extrapolation in accordancewith some embodiments; and

FIG. 10 illustrates an additional example of extrapolation in accordancewith some embodiments.

DETAILED DESCRIPTION

The following description and the drawings sufficiently illustratespecific embodiments to enable those skilled in the art to practicethem. Other embodiments may incorporate structural, logical, electricalprocess, and other changes. Portions and features of some embodimentsmay be included in, or substituted for, those of other embodiments.Embodiments set forth in the claims encompass all available equivalentsof those claims.

FIG. 1 illustrates an example of a device in accordance with someembodiments. In some embodiments, the device 100 may be or may be partof a radar device, a sonar device, a communication device, asurveillance device, a piece of equipment, a piece of test equipment orany other suitable type of device. As an example, a radar device may beused to determine motion, speed, position, topology and/or other aspectsof various elements in a physical environment. As another example, asonar device may be used to determine similar aspects of elements inenvironments that may include, but are not limited to, underwaterenvironments. In the embodiments described herein, the device 100 mayalso be referred to as a frequency data extrapolator. Alternatively,portions of the device 100 may be referred to collectively as afrequency data extrapolator.

It should be noted that embodiments are not limited to the exampledevice 100 shown in FIG. 1, in terms of number, type, name and/orarrangement of components. Some embodiments may not necessarily includeall components shown in the example device 100. Some embodiments mayinclude additional components not shown in the example device 100. Insome embodiments, one or more components may be used in place of one ormore components shown in the example device 100 and may provide same orsimilar functionality to components shown in the example device 100.

In some embodiments, the example device 100 may include one or moreantennas 101. The antenna 101 may be configured to transmit and/orreceive signals, in some cases. In some embodiments, the example device100 may include one or more sensors 102. As a non-limiting example, acoherently pulsed sensor 102 may be used. Although embodiments may bedescribed herein in terms of a single sensor 102, it is understood thatmultiple sensors 102 and/or a combination of sensors 102 may be used insome embodiments. The sensor 102 may be configured to transmit and/orreceive signals, in some cases, although the scope of embodiments is notlimited in this respect. In some embodiments, the device 100 may notnecessarily include the antenna 101, such as embodiments in which thesensor 102 may perform transmission and/or reception operations. In someembodiments, a combination of one or more antennas 101 and one or moresensors 102 may be included in the device 100. The antenna(s) 101, insuch embodiments, may be coupled to the sensors 102 (such as throughinterface circuitry 110 of the device) to provide received signals tothe sensors 102 and/or to receive signals from the sensors 102 fortransmission. The interface circuitry 110 may connect one or more of thecomponents of the device 100 to each other and/or to externalcomponents. The interface circuitry 110 may be wired, in someembodiments, although other configurations, such as wireless or optical,may be used in some embodiments.

The device 100 may also include processing circuitry 106 and memory 108arranged to perform operations described herein. In some embodiments,the device 100 may be a frequency data extrapolator, which may beconfigured to perform various operations described herein. In someembodiments, one or more components of the device 100 may be configuredto perform one or more operations related to frequency dataextrapolation and/or frequency data processing, such as those describedherein and/or others. As an example, processing circuitry 106, memory108 and/or other components of a device 100, such as a radar device, maybe configured to perform one or more of operations described hereinrelated to frequency data extrapolation and/or other operations. Asanother example, a frequency data extrapolator may include one or moreof the components of the device 100, such as processing circuitry 106,memory 108 and/or others. As another example, the frequency dataextrapolator may be implemented using one or more of the components ofthe device 100, such as processing circuitry 106, memory 108 and/orothers, and those components may implement other operations that may ormay not be related to frequency data extrapolation and/or frequency dataprocessing.

As used herein, the term “circuitry” may refer to, be part of, orinclude an Application Specific Integrated Circuit (ASIC), an electroniccircuit, a processor (shared, dedicated, or group), and/or memory(shared, dedicated, or group) that execute one or more software orfirmware programs, a combinational logic circuit, and/or other suitablehardware components that provide the described functionality. In someembodiments, the circuitry may be implemented in, or functionsassociated with the circuitry may be implemented by, one or moresoftware or firmware modules. In some embodiments, circuitry may includelogic, at least partially operable in hardware. Embodiments describedherein may be implemented into a system using any suitably configuredhardware and/or software. The machine readable medium 122 may be used toimplement one or more operations described herein, such as thosedescribed herein as performed by the frequency data processor and/ordevice 100, in some cases.

Any one or more of the techniques, operations, methods and/ormethodologies discussed herein may be performed on such a device 100, insome embodiments. In alternative embodiments, the device 100 may operateas a standalone device or may be connected (e.g., networked) to otherdevices. In a networked deployment, the device 100 may operate in thecapacity of a server machine, a client machine, or both in server-clientnetwork environments. In an example, the device 100 may act as a peermachine in peer-to-peer (P2P) (or other distributed) networkenvironment. In some embodiments, the device 100 may be a radar device,sonar device, personal computer (PC), a tablet PC, a set-top box (STB),a personal digital assistant (PDA), a mobile device, a base station, amobile telephone, a smart phone, a web appliance, a network router,switch or bridge, or any machine capable of executing instructions(sequential or otherwise) that specify actions to be taken by thatdevice. Further, while only a single device is illustrated, the term“device” shall also be taken to include any collection of devices thatindividually or jointly execute a set (or multiple sets) of instructionsto perform any one or more of the methodologies discussed herein, suchas cloud computing, software as a service (SaaS), other computer clusterconfigurations.

Examples, as described herein, may include, or may operate on, logic ora number of components, modules, or mechanisms. Modules are tangibleentities (e.g., hardware) capable of performing specified operations andmay be configured or arranged in a certain manner. In an example,circuits may be arranged (e.g., internally or with respect to externalentities such as other circuits) in a specified manner as a module. Inan example, the whole or part of one or more computer systems (e.g., astandalone, client or server computer system) or one or more hardwareprocessors may be configured by firmware or software (e.g.,instructions, an application portion, or an application) as a modulethat operates to perform specified operations. In an example, thesoftware may reside on a machine readable medium. In an example, thesoftware, when executed by the underlying hardware of the module, causesthe hardware to perform the specified operations.

Accordingly, the term “module” is understood to encompass a tangibleentity, be that an entity that is physically constructed, specificallyconfigured (e.g., hardwired), or temporarily (e.g., transitorily)configured (e.g., programmed) to operate in a specified manner or toperform part or all of any operation described herein. Consideringexamples in which modules are temporarily configured, each of themodules need not be instantiated at any one moment in time. For example,where the modules comprise a general-purpose hardware processorconfigured using software, the general-purpose hardware processor may beconfigured as respective different modules at different times. Softwaremay accordingly configure a hardware processor, for example, toconstitute a particular module at one instance of time and to constitutea different module at a different instance of time.

As a non-limiting example, a module may include a group of componentsconnected to (permanently, temporarily and/or semi-permanently) acircuit board, processor board and/or other medium.

The processing circuitry 106 may be or may include a hardware processor,such as a central processing unit (CPU), a graphics processing unit(GPU), a hardware processor core, or any combination thereof. The device100 may include a main memory 108 and a static memory 109, some or allof which may communicate with each other via the interface circuitry110. In some embodiments, components of the device 100 may communicatewith each other via the interface circuitry 110. The interface circuitry110 may include wired connections, in some embodiments, such asconnections between components of the device 100.

The device 100 may further include a display unit 111, which may providevideo display. The device 100 may include an alphanumeric input device112 (e.g., a keyboard), and a user interface (UI) navigation device 114(e.g., a mouse). In an example, the display unit 111, input device 112and/or UI navigation device 114 may be or may include a touch screendisplay. The device 100 may additionally include a storage device 116(e.g., drive unit), a signal generation device 118 (e.g., a speaker) foraudio output and/or a network interface device 125. The device 100 mayinclude an output controller 128, such as a serial (e.g., universalserial bus (USB), parallel, or other wired or wireless (e.g., infrared(IR), near field communication (NFC), etc.) connection to communicate orcontrol one or more peripheral devices (e.g., a printer, card reader,etc.).

The storage device 116 may include a machine readable medium 122 onwhich may be stored one or more sets of data structures or instructions124 (e.g., software) embodying or utilized by any one or more of thetechniques or functions described herein. The instructions 124 may alsoreside, completely or at least partially, within the main memory 108,within static memory 109, or within the processing circuitry 106 duringexecution thereof by the device 100.

In an example, one or any combination of the processing circuitry 106,the main memory 108, the static memory 109, or the storage device 116may constitute machine readable media. While the machine readable medium122 is illustrated as a single medium, the term “machine readablemedium” may include a single medium or multiple media (e.g., acentralized or distributed database, and/or associated caches andservers) configured to store the one or more instructions 124.

The term “machine readable medium” may include any medium that iscapable of storing, encoding, or carrying instructions for execution bythe device 100 and that cause the device 100 to perform any one or moreof the techniques of the present disclosure, or that is capable ofstoring, encoding or carrying data structures used by or associated withsuch instructions. Non-limiting machine readable medium examples mayinclude solid-state memories, and optical and magnetic media. Specificexamples of machine readable media may include: non-volatile memory,such as semiconductor memory devices (e.g., Electrically ProgrammableRead-Only Memory (EPROM). Electrically Erasable Programmable Read-OnlyMemory (EEPROM)) and flash memory devices; magnetic disks, such asinternal hard disks and removable disks; magneto-optical disks; RandomAccess Memory (RAM); and CD-ROM and DVD-ROM disks. In some examples,machine readable media may include non-transitory machine readablemedia. In some examples, machine readable media may include machinereadable media that is not a transitory propagating signal. In someembodiments, the term “computer readable storage medium” may be used todescribe such a medium.

The instructions 124 may further be transmitted or received over acommunications network 126 using a transmission medium via the networkinterface device 125 utilizing any one of a number of transfer protocols(e.g., frame relay, internet protocol (IP), transmission controlprotocol (TCP), user datagram protocol (UDP), hypertext transferprotocol (HTTP), etc.). Example communication networks may include alocal area network (LAN), a wide area network (WAN), a packet datanetwork (e.g., the Internet), mobile telephone networks (e.g., cellularnetworks), Plain Old Telephone (POTS) networks, and wireless datanetworks (e.g., Institute of Electrical and Electronics Engineers (IEEE)802.11 family of standards known as Wi-Fi®. IEEE 802.16 family ofstandards known as WiMax®). IEEE 802.15.4 family of standards, a LongTerm Evolution (LTE) family of standards, a Universal MobileTelecommunications System (UMTS) family of standards, peer-to-peer (P2P)networks, among others. In an example, the network interface device 125may include one or more physical jacks (e.g., Ethernet, coaxial, orphone jacks) or one or more antennas to connect to the communicationsnetwork 126. In an example, the network interface device 125 may includea plurality of antennas to wirelessly communicate using at least one ofsingle-input multiple-output (SIMO), multiple-input multiple-output(MIMO), or multiple-input single-output (MISO) techniques. In someexamples, the network interface device 125 may wirelessly communicateusing Multiple User MIMO techniques. The term “transmission medium”shall be taken to include any intangible medium that is capable ofstoring, encoding or carrying instructions for execution by the device100, and includes digital or analog communications signals or otherintangible medium to facilitate communication of such software.

Although the device 100 is illustrated as having several separatefunctional elements, one or more of the functional elements may becombined and may be implemented by combinations of software-configuredelements, such as processing elements including digital signalprocessors (DSPs), and/or other hardware elements. For example, someelements may comprise one or more microprocessors, DSPs,field-programmable gate arrays (FPGAs), application specific integratedcircuits (ASICs), radio-frequency integrated circuits (RFICs) andcombinations of various hardware and logic circuitry for performing atleast the functions described herein. In some embodiments, thefunctional elements may refer to one or more processes operating on oneor more processing elements. Embodiments may be implemented in one or acombination of hardware, firmware and software. Embodiments may also beimplemented as instructions stored on a computer-readable storagedevice, which may be read and executed by at least one processor toperform the operations described herein. A computer-readable storagedevice may include any non-transitory mechanism for storing informationin a form readable by a machine (e.g., a computer). For example, acomputer-readable storage device may include read-only memory (ROM),random-access memory (RAM), magnetic disk storage media, optical storagemedia, flash-memory devices, and other storage devices and media. Someembodiments may include one or more processors and may be configuredwith instructions stored on a computer-readable storage device.

FIG. 2 illustrates an example of pulsed sensor operation in accordancewith some embodiments. FIG. 3 illustrates examples of a compressed imagedomain and a dispersed Fourier domain in accordance with someembodiments. It should be noted that the examples shown in FIGS. 2-3 mayillustrate some or all of the concepts and techniques described hereinin some cases, but embodiments are not limited by the examples. Forinstance, embodiments are not limited by the name, number, type, size,ordering, arrangement and/or other aspects of the pulses, collectionwindows, times, time indexes, time dimensions (such as fast time andslow time), frequency dimensions (such as fast time frequency and slowtime frequency) and/or other elements as shown in FIGS. 2-3.

Referring to FIG. 2, in the example scenario 200, a sequence of timepulses 205 may be transmitted by the sensor 102. Periodic transmission,in accordance with a periodicity interval 208, of the pulses 205 may beused in some embodiments. In addition, the pulses 205 may also be of afixed time duration 207 in some embodiments. In some cases, theperiodicity parameter 208 may be much larger than the time duration 207,such as by one or two orders of magnitude. It should be noted thatembodiments are not limited to periodic transmission or to fixedduration transmission. In an example, electromagnetic (EM) pulses may beused in some applications, such as radar. In another example, pulsesbased on soundwaves, may be used in some applications, such as sonar. Itshould be noted, however, that embodiments are not limited to usage ofEM pulses or pulses based on soundwaves.

The sensor 102 may receive and/or collect signals during collectionwindows 210. As a non-limiting example, the signals may be returnsignals that result from transmitted pulses 205. The return signals maybe affected by the environment, such as by objects in the environment.For instance, when a pulse 205 is transmitted, a return signal mayinclude a portion of the transmitted energy that was reflected back tothe sensor 102 by an object in the environment. The return signal mayalso be spread, smeared and/or otherwise distorted in comparison to theoriginal pulse 205. As an example, a relatively narrow time pulse may bepartly reflected back to the sensor 102 as a distorted shape that is ofhighly reduced energy in comparison to the original pulse 205 andspread/distorted in time in comparison to the original pulse 205. Insome embodiments, the device 100 may be able to determine informationabout the environment based on the effects exhibited in the returnsignals. For instance, one or more parameters of the physicalenvironment may be determined, including but not limited to motion,speed, acceleration, position, topology and/or other aspects of variouselements in a physical environment. Such parameters may also includetopology, atmospheric pressure, atmospheric aspects and/or otherparameters related to the physical environment. It should be noted thatthe transmission of the pulses and collection/reception of the returnsignals may be performed by the sensor 102 in some embodiments. However,the device 100 and/or other components of the device 100 (such as anantenna 101) may also be used for this purpose, in some embodiments.

Referring to FIG. 3, the example 300 shows a compressed image domain 310and a dispersed Fourier domain 320. In some embodiments, the domains 310and 320 may be related by a two-dimensional Fourier Transform (FT) and atwo-dimensional inverse FT, as indicated by 330. In a non-limitingexample, the x-axis of the compressed image domain 310 may represent aslow time dimension 314 and the y-axis of the compressed image domain310 may represent a fast time dimension 312. The x-axis of the dispersedFourier domain 320 may represent a slow time frequency dimension 324 andthe y-axis of the dispersed Fourier domain 320 may represent a fast timefrequency dimension 322.

The slow time dimension 314 may be based on time indexes/counts of thepulses 205 while the fast time dimension 312 may be based on a timescale, such as a length or duration, of the collection window 210.Accordingly, for a particular time pulse 205, a column of the compressedimage domain 310 may include complex values that are based on a returnsignal collected at the sensor 102 during the collection window 210immediately following the particular time pulse 205. Columns of thecompressed image domain 310 may be based on successive return signalsbased on successive time pulses 205. The values of the compressed imagedomain 310 and/or dispersed Fourier domain 320 may be complex, in someembodiments. However, embodiments are not limited to complex values foreither of the compressed image domain 310 and/or dispersed Fourierdomain 320.

In some embodiments, processing may be performed in the compressed imagedomain 310 and/or dispersed Fourier domain 320. In some cases, aprocessing operation may be easier, faster, more efficient and/orotherwise more applicable in one of the dimensions. As an example, aconvolution operation in a first of the domains may be performed in thesecond of the domains using multiplication operations, in some cases.Accordingly, it may be preferable to perform processing in the seconddomain, in this particular case, as multiplication may be lesscomputationally intense than convolution. In some embodiments, variousimaging effects may be more pronounced in a first of the domains incomparison to the second domain, in which case operations may beperformed in the first domain.

In accordance with some embodiments, the frequency data extrapolator mayreceive input frequency data mapped to a two-dimensional frequency grid.As an example, the input frequency data may be based on return signalsreceived, at a sensor of the device 100, in response to pulsedtransmissions of the sensor in a physical environment. Regions of thefrequency grid may be classified as high fidelity or low fidelity. Agroup of basis rectangles may be determined within the high fidelityregions. A column-wise extrapolation matrix and a row-wise extrapolationmatrix may be determined based on the input frequency data of the basisrectangles. The input frequency data of the high fidelity regions may beextrapolated to replace the input frequency data of the low fidelityregions. These embodiments will be described in more detail below.

It should be noted that references herein to extrapolation and/orextrapolation operations are not limiting. Other techniques, such asinterpolation, extension, approximation and/or others may be used insome embodiments. In addition, a combination of one or more ofextrapolation, interpolation, extension, approximation and/or othertechniques may be used in some embodiments. As an example, a value for aparticular pixel of a two-dimensional grid may be replaced by a valuethat is based on values of other pixels in the grid. For instance, theother pixels may include pixels near the particular pixel or regions ofpixels that surround the particular pixel. Depending on locations of theother pixels with respect to the particular pixel, the determination ofthe value for the particular pixel may be considered an extrapolation,an interpolation or a combination thereof. Although the term“extrapolation” may be used herein to describe this operation and/orother operations, the scope of embodiments is not limited by usage ofthe term “extrapolation.”

FIG. 4 illustrates the operation of an example method of frequencydomain extrapolation of sensor data in accordance with some embodiments.In some embodiments, the method 400 may be performed by the device 100.One or more components of the device 100 may perform one or moreoperations of the method 400, in some embodiments. As an example, theprocessing circuitry 106 may perform one or more operations of themethod 400, including but not limited to operations that are related toextrapolation of frequency data. As another example, the frequency dataextrapolator described previously may perform one or more operations ofthe method 400, including but not limited to operations that are relatedto extrapolation of frequency data. As another example, the sensor 102may perform transmission, reception and/or collection operations of themethod 400. Embodiments are not limited by these examples, however, asoperations may be performed by other components and/or other devices, insome embodiments.

It is important to note that embodiments of the method 400 may includeadditional or even fewer operations or processes in comparison to whatis illustrated in FIG. 4. In addition, embodiments of the method 400 arenot necessarily limited to the chronological order that is shown in FIG.4. In describing the method 400, reference may be made to FIGS. 1-3 and5-10, although it is understood that the method 400 may be practicedwith any other suitable systems, interfaces and components. It shouldalso be noted that the method 400 may be applicable to an apparatus forthe device 100, in some embodiments.

FIGS. 5-10 illustrate examples that may be applicable to someembodiments. FIG. 5 illustrates additional examples of a compressedimage domain and a dispersed Fourier domain in accordance with someembodiments. FIG. 6 illustrates an example of a group of basisrectangles in accordance with some embodiments. FIG. 7 illustrates anexample of determination of extrapolation matrixes in accordance withsome embodiments. FIGS. 8-10 illustrate examples of extrapolation inaccordance with some embodiments. It should be noted that the examplesshown in FIGS. 5-10 may illustrate some or all of the concepts andtechniques described herein, in some cases, but embodiments are notlimited by the examples. For instance, embodiments are not limited bythe name, number, type, size, ordering, arrangement and/or other aspectsof the frequency grid, frequency data, time data, extrapolationmatrixes, extrapolation techniques, basis rectangles, other rectangles,regions of the frequency grid and/or other elements as shown in FIGS.5-10.

At operation 405 of the method 400, the processing circuitry 106 mayreceive input frequency data mapped to a two-dimensional frequency grid.In some embodiments, the input frequency data may be received from thecoherently pulsed sensor 102 and may be based on return signals frompulsed transmissions of the sensor 102, although the scope ofembodiments is not limited in this respect. As a non-limiting example,pulsed transmissions such as those illustrated in FIG. 2 may beperformed by the coherently pulsed sensor 102, and return signals may bemapped to a compressed image domain (such as 310 in FIG. 3) and/ordispersed Fourier domain (such as 320 in FIG. 3). Additional examples ofa compressed image domain 550 and a dispersed Fourier domain 500 areshown in FIG. 5.

As another non-limiting example, the input frequency data may be mappedto the frequency grid in a dispersed Fourier format that is based on atwo-dimensional Fourier transform of two-dimensional compressed imagedata from the sensor 102. Each column of the compressed image data maybe based on a return signal from one of the pulsed transmissions of thesensor 102. The columns may be based on sequential return signals inchronological order, in some cases. For instance, a first column may bebased on a first chronological return signal, a second column may bebased on a second chronological return signal and the relationship maybe extended for subsequent columns.

At operation 410, the processing circuitry 106 may classify regions ofthe frequency grid as high fidelity or low fidelity. An example of suchis shown in FIG. 5, in which the regions 520 (of the lighter, gray andwhite colors) may be classified as high fidelity and the regions 525 (ofthe darker, black color) may be classified as low fidelity. Anotherexample of such is shown by the frequency grid 600 shown in FIG. 6, inwhich the regions 605 (demarcated by the gray color) may be classifiedas high fidelity and the regions 610 (demarcated by the black color, andlocated between the regions 605) may be classified as low fidelity. Theregions 615 (demarcated by the black color, and located outside of theregions 605 and 610) may be regions of the frequency grid 600 that arezero padded. The zero padding may be performed for purposes such asachievement of a Nyquist sampling rate and/or other purpose.

It should be noted that embodiments are not limited to twoclassifications and are also not limited to the particularclassifications of high fidelity and low fidelity. For instance, othercategories, such as valid/invalid, good/bad, present/missing,present/absent or other may be used.

The classification may be based at least partly on one or more fidelitymeasurements of the input frequency data, in some cases. Themeasurements may be performed for individual pixels of the frequencygrid, regions of pixels (such as contiguous regions of pixels) in thefrequency grid, any suitable grouping of the pixels and/or any suitabledivision of the frequency grid. In some embodiments, the frequency gridmay be divided, based on fidelity measurements of the pixels, into agroup of one or more low fidelity regions and a group of high fidelityregions. The regions in this example may include contiguous groups ofthe pixels.

Examples of fidelity measurements may include amplitude level, powerlevel, signal level, signal quality level, noise level artifact leveland/or other measurements. As an example, fidelity measurements of theinput frequency data may include amplitude measurements of the inputfrequency data, and regions may be classified as high fidelity or lowfidelity based at least partly on comparisons of the amplitudemeasurements with a predetermined amplitude threshold. For instance,referring to FIG. 5, the power scale (given in dB) at the right side ofthe dispersed Fourier domain 500 indicates that colors of pixels in thegrid 500 become darker as the amplitude and/or power decreases. Thevalue in dB may be with respect to a peak amplitude/power of all pixelsof the grid 500, an average amplitude/power of all pixels of the grid500 or other suitable parameter. As an example, the darkest regions 525may be considered low fidelity regions and the lighter regions 520 maybe considered high fidelity regions. A threshold, such as −30 dB, −40 dBor other suitable value (including scalar values and/or non-dB values)may be used, in which case pixels/regions for which amplitudes/powersare below the threshold may be classified as low fidelity. Otherpixels/regions for which amplitudes/powers are above or equal to thethreshold may be classified as high fidelity. In some cases, such athreshold may be predetermined, although the scope of embodiments is notlimited in this respect. Embodiments are not limited to these examples,however, as other suitable measurements and/or techniques may be used toclassify the regions. In some embodiments, it may be determined that theinput frequency data in a group of one or more regions is missing, forany suitable reason. In such cases, those regions may be treated in asimilar manner as the low fidelity regions.

At operation 415, the processing circuitry 106 may determine a group ofbasis rectangles within the high fidelity regions. As will be describedbelow in more detail, the basis rectangles may be used, in someembodiments, to determine one or more parameters of an extrapolationmodel. Referring to FIG. 6, a non-limiting example of basis rectangles630 included in the high fidelity regions 605 is illustrated.

In some embodiments, the high fidelity regions (such as a combinedregion) may be divided to include a group of non-overlapping basisrectangles of a same basis rectangle size. In such cases, it isunderstood that one or more “leftover” portions may result, as the highfidelity regions may not necessarily be rectangle, straight or otherwiseuniform, and therefore may not be completely covered by a group of basisrectangles.

In some embodiments, the group of basis rectangles may be restricted toa group of non-overlapping rectangles of a same basis rectangle size.The rectangle size may include a pair of dimensions, such as a lengthand height, a number of pixels in each of two dimensions, a length interms of an x-coordinate and a length in terms of a y-coordinate and/orother pair. The group of basis rectangles may be determined inaccordance with a joint maximization of a basis rectangle area and aportion of the high fidelity regions covered by the basis rectangles, insome cases.

As a non-limiting example, the processing circuitry 106 may generatemultiple candidate groups of non-overlapping basis rectangles within thehigh fidelity regions (such as at operation 420). In some cases, thecandidate groups may be generated by arbitrarily choosing from among themany possible configurations of basis rectangles, although the scope ofembodiments is not limited in this respect. Within each candidate group,a basis rectangle size may be the same. But the basis rectangle set ofat least some of the candidate groups may be different. That is, therectangle size may be varied across candidate groups but may be the samewithin each candidate group. In addition, locations of the rectangles ofeach candidate groups may be varied across the candidate groups, in somecases. It may be desired, in some cases, that the rectangle size (or anarea of the rectangle) be as large as possible. Accordingly, rectanglearea may be a criterion used, in some embodiments, in selecting thegroup of basis rectangles from the candidate groups. As a non-limitingexample of selection of the basis rectangles in accordance with a jointcriterion, if a total area covered by the basis rectangles is greaterthan a predetermined threshold, such as 50% (or any suitable percentageand/or quantity) of the area of the high fidelity regions, then amaximization of the area of each basis rectangle may be prioritized.Otherwise, a maximization of the total area covered by the basisrectangles may be prioritized.

Other criteria may be used, in addition to or instead of, the rectanglesize or rectangle area. As an example, an amount of area covered by eachcandidate group may also be used. The coverage may be given ordetermined in terms of an area of the frequency grid, a percentage(ratio) of the frequency grid, a percentage (ratio) of the high fidelityregions and/or other suitable measurement.

It should be noted that, as the rectangles may be restricted tonon-overlapping rectangles within a limited area (the high fidelityregions), a number of such rectangles that may fit into the limited areamay be related to the rectangle size. For instance, as the rectanglesize increases, a number of rectangles that can fit into the limitedarea may decrease (or at least not increase). Accordingly, a number ofrectangles in each candidate group may be variable and may be a functionof rectangle size, size of the high fidelity regions, layout (shape) ofthe high fidelity regions and/or other factors.

It should be noted that the group of basis rectangles may be selectedfrom the candidate groups in accordance with a trade-off betweenrectangle size and coverage, in which it may be desired that both be aslarge as possible. However, as noted above, a number of rectangles thatcan fit into the limited area may decrease as the rectangle sizeincreases. Therefore, the coverage ratio may also decrease. In someembodiments, one or more thresholds, such as minimum size, minimum basisrectangle area, minimum coverage and/or others may be used for selectionof the group of basis rectangles from the candidate groups. Forinstance, one or more thresholds may be used in combination, in somecases.

As a non-limiting example, the processing circuitry 106 may select aportion of the candidate groups for which total areas covered by thebasis rectangles of the candidate groups are greater than apredetermined coverage threshold at operation 425. The processingcircuitry 106 may select the group of basis rectangles as a candidategroup from the portion based on the basis rectangle area of eachcandidate group at operation 430. For instance, the group (or one of thegroups) with maximum basis rectangle area may be selected. Theseexamples are not limiting, however, as other techniques may be used toselect the group of basis rectangles.

At operation 435, the processing circuitry 106 may determine acolumn-wise extrapolation matrix and a row-wise extrapolation matrix.The matrixes may be of a same size (in terms of rows and columns ofpixels) as the basis rectangles. The matrixes may be determined for atwo-dimensional extrapolation of the input frequency data of the highfidelity regions to replace the input frequency data of the low fidelityregions, in some cases.

As a non-limiting example, columns of the column-wise extrapolationmatrix may be determined per column based on the input frequency data ofcorresponding columns of the basis rectangles. That is, a particularcolumn of the column-wise extrapolation matrix may be determined usingthe input frequency data of the same column within each of the basisrectangles (or in each of at least a portion of the basis rectangles).For instance, the columns of the column-wise extrapolation matrix may benumbered by a sequence of column indexes (such as 1, 2, . . . . N). Thecolumns of each basis rectangle may also be numbered in the same manner.For each column index, the column of the column-wise extrapolationmatrix for that particular index may include a set of weights determinedbased on the input frequency data of the columns of the basis rectanglesmapped to the particular index. For instance, the values of column #1 ofthe column-wise extrapolation matrix may be based on the input frequencydata in column #1 of all (or at least some) of the basis rectangles. Thevalues of column #2 of the column-wise extrapolation matrix may be basedon the input frequency data in column #2 of all (or at least some) ofthe basis rectangles. This relationship may be extended to the N columnsof the column-wise extrapolation matrix and basis rectangles.

A non-limiting example of the technique described above is shown in FIG.7. For instance, the values of column #1 (741) of the column-wiseextrapolation matrix 740 may be based on the input frequency data incolumn #1 of all (or at least some) of the basis rectangles 731-735. Thevalues of column #2 (742) of the column-wise extrapolation matrix 740may be based on the input frequency data in column #2 of all (or atleast some) of the basis rectangles 731-735. This relationship may beextended to the N columns of the column-wise extrapolation matrix 740and basis rectangles 731-735.

Any suitable technique may be used to determine the values of thecolumn-wise extrapolation matrix. As a non-limiting example, the valuesfor a particular column may be based on correlations between the inputfrequency data of corresponding columns of the basis rectangles.Techniques such as a Burg algorithm. Yule-Walker algorithm, Wiener-Hopfalgorithm, linear prediction algorithm other algorithms and/or acombination thereof may be used, in some cases. In some embodiments, oneor more values of the extrapolation matrixes may be complex. However,the scope of embodiments is not limited in this respect, as real valuesmay be applicable, in some cases.

Analogous, similar, or the same techniques used for the determination ofthe column-wise extrapolation matrix may be used to determine therow-extrapolation matrix. For instance, rows of the row-wiseextrapolation matrix may be determined per row based on the inputfrequency data of corresponding rows of the basis rectangles. That is, aparticular row of the row-wise extrapolation matrix may be determinedusing the input frequency data of the same row within each of the basisrectangles (or in each of at least a portion of the basis rectangles).For instance, the rows of the row-wise extrapolation matrix may benumbered by a sequence of row indexes (such as 1, 2, . . . . M) and therows of each basis rectangle may be numbered in the same manner. Foreach row index, the row of the row-wise extrapolation matrix for thatparticular index may include a set of weights determined based on theinput frequency data of the rows of the basis rectangles mapped to theparticular index. For instance, the values of row #1 of the row-wiseextrapolation matrix may be based on the input frequency data in row #1of all (or at least some) of the basis rectangles. The values of row #2of the row-wise extrapolation matrix may be based on the input frequencydata in row #2 of all (or at least some) of the basis rectangles. Thisrelationship may be extended to the M rows of the row-wise extrapolationmatrix and basis rectangles.

The non-limiting example of FIG. 7 may also be used to illustrate thetechnique described above for the row-wise extrapolation matrix 750. Forinstance, the values of row #1 (751) of the row-wise extrapolationmatrix 750 may be based on the input frequency data in row #1 of all (orat least some) of the basis rectangles 731-735. The values of row #2(752) of the row-wise extrapolation matrix 750 may be based on the inputfrequency data in row #2 of all (or at least some) of the basisrectangles 731-735. This relationship may be extended to the M rows ofthe row-wise extrapolation matrix 750 and basis rectangles 731-735.

Any suitable technique may be used to determine the values of therow-wise extrapolation matrix. As a non-limiting example, the values fora particular row may be based on correlations between the inputfrequency data of corresponding rows of the basis rectangles. Techniquessuch as a Burg algorithm, Yule-Walker algorithm. Wiener-Hopf algorithm,linear prediction algorithm, other algorithms and/or a combinationthereof may be used, in some cases

At operation 440, the processing circuitry 106 may extrapolate frequencydata using the column-wise extrapolation matrix and/or row-wiseextrapolation matrix. One or more extrapolation rectangles of a samesize as the basis rectangles may be determined. In some embodiments, theextrapolation rectangles may be the same as the basis rectangles,although the scope of embodiments is not limited in this respect. Anysuitable group of extrapolation rectangles may be used. As an example,one or more extrapolation rectangles may be selected to be near aparticular low fidelity region. As another example, one or moreextrapolation rectangles may be selected to surround a particular lowfidelity region. It should be noted that embodiments are not limited bythese examples.

Multiple examples of techniques and/or operations that may be used aspart of extrapolation will be described below. It should be noted thatsome embodiments may include a combination of one or more of thosetechniques and/or operations. In addition, in some embodiments, one ormore additional techniques and/or operations may be used.

Extrapolation from the extrapolation rectangles in accordance with thecolumn-wise extrapolation matrix and/or row-wise extrapolation matrixmay be performed. Extrapolation in an upward or downward direction (suchas along a column of the frequency grid) may be performed using thecolumn-wise extrapolation matrix. Extrapolation in a leftward orrightward direction (such as along a row of the frequency grid) may beperformed using the row-wise extrapolation matrix.

In some embodiments, one or more operations described below may beperformed as part of an extrapolation of the input frequency data of theextrapolation rectangle to replace the input frequency data of a groupof low fidelity pixels of the low fidelity regions. For a low fidelitypixel above or below a particular column of the extrapolation rectanglein the frequency grid, a sum of the input frequency data of theparticular column of the extrapolation rectangle weighted by acorresponding column of the column-wise extrapolation matrix may bedetermined. For a low fidelity pixel to the left or to the right of aparticular row of the extrapolation rectangle in the frequency grid, asum of the input frequency data of the particular row of theextrapolation rectangle weighted by a corresponding row of the row-wiseextrapolation matrix may be determined.

In some embodiments, one or more operations described below may beperformed as part of an extrapolation of the input frequency data of theextrapolation rectangle to replace the input frequency data of a groupof low fidelity pixels of the low fidelity regions. For instance,referring to the scenario 800 shown in FIG. 8, in the frequency grid805, extrapolation from the rectangle 820 may be performed in the upwarddirection and extrapolation from the rectangle 830 may be performed inthe leftward direction. Accordingly, possible frequency values forpixels in the region 810 may be determined based on either or both ofthe extrapolations from rectangles 820, 830.

For upward or downward extrapolation, the input frequency data of thepixels of the extrapolation rectangle may be extrapolated into a groupof rows of pixels immediately above or below the extrapolationrectangle. For instance, between one and M rows may be included in thegroup when the extrapolation matrix has M rows. The extrapolation may beperformed in sequence, with extrapolated rows stored for usage inextrapolation of subsequent rows (either above or below).

For instance, referring to 910 of FIG. 9, when extrapolation isperformed in the downward direction 915, the input frequency data ofrows 1 through M may be extrapolated into row M+1. The input frequencydata of rows 2 through M+1 may be extrapolated into row M+2. Thisprocess may continue for rows subsequent to row M+2 (below M+2 in thefrequency grid 900, in this case). Referring to 920 of FIG. 9, whenextrapolation is performed in the upward direction 925, the inputfrequency data of rows 1 through M may be extrapolated into row M+1. Theinput frequency data of rows 2 through M+1 may be extrapolated into rowM+2. This process may continue for rows subsequent to row M+2 (above M+2in the frequency grid 900, in this case).

Extrapolation in the leftward and rightward directions may be performedin an analogous or similar manner, in some embodiments. For leftward orrightward extrapolation, the input frequency data of the pixels of theextrapolation rectangle may be extrapolated into a group of columns ofpixels immediately to the left or right of the extrapolation rectangle.For instance, between one and N columns may be included in the groupwhen the extrapolation matrix has N columns. The extrapolation may beperformed in sequence, with extrapolated columns stored for usage inextrapolation of subsequent columns (either to the left or right).

Referring to 930 of FIG. 9, when extrapolation is performed in theleftward direction 935, the input frequency data of columns 1 through Nmay be extrapolated into column N+1. The input frequency data of columns2 through N+1 may be extrapolated into column N+2. This process maycontinue for columns subsequent to column N+2 (to the left of N+2 in thefrequency grid 900, in this case). Referring to 940 of FIG. 9, whenextrapolation is performed in the rightward direction 945, the inputfrequency data of columns 1 through N may be extrapolated into columnN+1. The input frequency data of columns 2 through N+1 may beextrapolated into column N+2. This process may continue for columnssubsequent to column N+2 (to the right of N+2 in the frequency grid 900,in this case).

Referring to FIG. 10, a non-limiting example of extrapolation inmultiple directions is shown. It should be noted that the order ofdirections in which the extrapolation is performed is not limited by theexample of FIG. 10. An original frequency grid 1005 of input frequencydata may include one or more low fidelity regions. An extrapolation inthe original grid 1010 in the upward direction may generate the grid1020. That is, extrapolation of all extrapolation rectangles in theupward direction may be performed. An extrapolation in the original grid1010 in the downward direction may generate the grid 1025. That is,extrapolation of all extrapolation rectangles in the upward directionmay be performed. A weighting of the two grids 1020 and 1025 may beperformed to generate a first grid 1030 of coherent, weighted meanvalues. As an example, for a pixel that is in a location of the originalgrid 1010 for which the upward and downward extrapolations produce anextrapolated result, a weighting such as those previously described(such as based on distances) may be used for the generation of the grid1030. In a similar manner, extrapolations of the grid 1030 may beperformed in the leftward and rightward directions to generate the grids1040 and 1045. A weighting similar to that used for the grid 1030 mayalso be used to generate a second grid 1050 of coherent, weighted meanvalues. It should be noted that the input frequency data in the highfidelity regions may not necessarily be replaced in the grid 1030 and/orgrid 1050.

It should also be noted that embodiments are not limited to performanceof the extrapolations and/or weightings in the order shown. As anexample, extrapolation in the leftward and rightward directions may beperformed, followed by a weighting, followed by extrapolations in theupward and downward directions, followed by another weighting. Asanother example, one or more extrapolations and/or weightings may beperformed in any order. For instance, extrapolations of leftward,upward, rightward, downward may be performed in sequence, followed by aweighting.

In some embodiments, one or more operations described below may beperformed as part of an extrapolation of the input frequency data of theextrapolation rectangle to replace the input frequency data of a groupof low fidelity pixels of the low fidelity regions. For eachextrapolation rectangle, the input frequency data of the extrapolationrectangle may be extrapolated in one or more candidate directions withrespect to the extrapolation rectangle, the candidate directions from agroup that includes above, below, to the left, and to the right. For apixel in which extrapolation in multiple candidate directions isperformed, the input frequency data of the pixel may be replaced with avalue based on a weighted sum of extrapolated values from the multipleextrapolations. In some cases, for a particular pixel, multipleextrapolations may provide candidate frequency values for the pixel, anda weighted sum may be used. In such cases, weights used for the weightedsum may be based at least partly on distances between the pixel and theextrapolation rectangles from which the pixels are extrapolated.

In some embodiments, multiple directions of extrapolation may be used.As an example, values for the low fidelity region 725 may beextrapolated from rectangle 732 in the leftward direction. In addition,values for the low fidelity region 720 may be extrapolated fromrectangle 731 in the upward direction and from rectangle 732 in theleftward direction. When different values for a pixel of a low fidelityregion (such as those in the region 720) are determined as a result ofmultiple extrapolations, the values may be combined in accordance with asuitable weighting. For instance, the weighting may be based ondistances from the pixel to the extrapolation rectangles from which themultiples extrapolations were performed. In the example of FIG. 7,rectangle 731 is closer to the region 720 than is rectangle 732.Therefore the weighting may be higher for the extrapolation fromrectangle 731 than for the extrapolation from rectangle 732, in somecases.

Referring to the scenario 800 shown in FIG. 8, in the frequency grid805, extrapolation from the rectangle 820 may be performed in the upwarddirection and extrapolation from the rectangle 830 may be performed inthe leftward direction. Accordingly, possible frequency values forpixels in the region 810 may be determined based on either or both ofthe extrapolations from rectangles 820, 830. As an example, for thepixel 815 of the region 810, a weighting of extrapolations fromrectangles 820 and 830 may be based on distances between the pixel 815and the rectangles 820 and 830. A first distance 825 between the pixel815 and the rectangle 820 and a second distance 835 between the pixel815 and the rectangle 830 may be used, in some cases. For instance,denote the first distance 825 as d1, the extrapolated frequency valuefrom rectangle 820 for pixel 815 as V1, the second distance 835 as d2,and the extrapolated frequency value from rectangle 830 for pixel 815 asV2. A combined extrapolated frequency value ofV=V1*d2/(d1+d2)+V2*d1/(d1+d2) may be used for the pixel 815. In somecases, it may be possible that extrapolations from more than tworectangles may be combined to determine a value for a particular pixel,in which case the above technique may be extended. It should be notedthat embodiments are not limited to this particular combining operationdescribed above for FIG. 8, as other suitable techniques for combiningtwo or more extrapolated values may be used in some embodiments.

Returning to the method 400, at operation 445, the processing circuitry106 may replace the input frequency data of low fidelity regions/pixelswith corresponding extrapolated frequency data (such as that describedabove). At operation 450, the processing circuitry 106 may refrain fromreplacement of the input frequency data of high fidelity regions/pixelswith corresponding extrapolated frequency data. In some embodiments, oneor more of operations 440, 445 and/or 450 may be used to generate outputfrequency data based on the input frequency data of the high fidelityregions and further based on the extrapolated frequency data of the lowfidelity regions. That is, the output frequency data may include and/orretain the input frequency data in the high fidelity regions, but mayreplace the input frequency data of the low fidelity regions withextrapolated frequency data, in some embodiments.

As an example, it may be convenient or efficient to perform operationssuch as extrapolation in accordance with a regular pattern, such as instraight rows, straight columns, rectangular regions or other. After theextrapolation, the input frequency data of regions/pixels of lowfidelity may be replaced by extrapolated frequency data and the inputfrequency data of regions/pixels of high fidelity may be retained. Forinstance, an extrapolation above a rectangle may be performed in aregion that is the same size as the rectangle itself, although theregion may include high fidelity and low fidelity pixels. After theextrapolation, the frequency data processor may replace the inputfrequency data of the low fidelity pixels and may refrain fromreplacement of the input frequency data of the high fidelity pixels.

At operation 455, an inverse Fourier transform may be performed togenerate an output compressed image. The inverse Fourier transform maybe performed on a set of output frequency data that includes theoriginal input frequency data in high fidelity regions and includesextrapolated frequency data in the low fidelity regions.

At operation 460, a parameter or other information, such as a physicalparameter of an environment, may be determined. The output frequencydata and/or the output compressed image of operation 455 may be used forsuch purposes. Examples of physical parameters may include, but are notlimited to, speed, position, size and/or type of an object in theenvironment into which the pulsed transmissions are performed.Additional examples may include, but are not limited to, topology,atmospheric pressure, atmospheric aspects and/or other parametersrelated to the physical environment. Radar techniques, sonar techniquesand/or other techniques may be used, in some embodiments.

It should be noted that, in some embodiments, the parameter of operation460 may be determined by the frequency data processor and/or the device100. In some embodiments, the parameter may be determined by anothercomponent, in which case the output frequency data, extrapolatedfrequency data, output compressed image (based at least partly on theextrapolated frequency data) and/or other information may be sent to theother component. As an example, the frequency data processor may beincluded in a chain of components of the device 100, and the output maybe passed to a next component in the chain for further processing. Thenext component and/or other component in the chain may determine theparameter, in some embodiments.

In Example 1, a frequency data extrapolator may comprise memory, such asmain memory 108, static memory 109, and/or the storage device of FIG. 1.The frequency data extrapolator may further comprise processingcircuitry, such as processing circuitry 106 of FIG. 1. The processingcircuitry may be configured to receive input frequency data mapped to atwo-dimensional frequency grid. The input frequency data may be based onreturn signals received at a sensor, such as sensor 102 of FIG. 1, inresponse to pulsed transmissions of the sensor in a physicalenvironment. The processing circuitry may be further configured toclassify regions of the frequency grid as high fidelity or low fidelitybased at least partly on fidelity measurements of the input frequencydata. The processing circuitry may be further configured to determine agroup of basis rectangles within the high fidelity regions. Theprocessing circuitry may be further configured to determine acolumn-wise extrapolation matrix and a row-wise extrapolation matrixbased on the input frequency data of the basis rectangles. Theprocessing circuitry may be further configured to generate outputfrequency data for usage in determination of a parameter of the physicalenvironment. The output frequency data may be generated based on atwo-dimensional extrapolation of the input frequency data of the highfidelity regions to replace the input frequency data of the low fidelityregions. The extrapolation may be in accordance with the column-wiseextrapolation matrix and a row-wise extrapolation matrix.

In Example 2, which extends the subject matter of Example 1, columns ofthe column-wise extrapolation matrix may be determined per column basedon the input frequency data of corresponding columns of the basisrectangles. Rows of the row-wise extrapolation matrix may be determinedper row based on the input frequency data of corresponding rows of thebasis rectangles.

In Example 3, based on the subject matter of one or any combination ofExamples 1-2, the output frequency data may be generated for usage indetermination of a parameter of the physical environment by a componentexternal to the frequency data extrapolator.

In Example 4, based on the subject matter of one or any combination ofExamples 1-3, the group of basis rectangles may be restricted to a groupof non-overlapping rectangles of a same basis rectangle size. The groupof basis rectangles may be determined in accordance with a jointmaximization of a basis rectangle area and a portion of the highfidelity regions covered by the basis rectangles.

In Example 5, based on the subject matter of one or any combination ofExamples 1-4, the processing circuitry may be further configured togenerate multiple candidate groups of non-overlapping basis rectanglesfor which basis rectangle sizes per candidate group are variable. Theprocessing circuitry may be further configured to select a first portionof the candidate groups for which total areas covered by the basisrectangles of the candidate groups are greater than a predeterminedcoverage threshold. The processing circuitry may be further configuredto select the group of basis rectangles as a candidate group from thefirst portion with a maximum basis rectangle area.

In Example 6, based on the subject matter of one or any combination ofExamples 1-5, the processing circuitry may be further configured todetermine an extrapolation rectangle within the high fidelity regions.The processing circuitry may be further configured to, as part of anextrapolation of the input frequency data of the extrapolation rectangleto replace the input frequency data of a group of low fidelity pixels ofthe low fidelity regions: when at least a first low fidelity pixel isabove or below a particular column of the extrapolation rectangle in thefrequency grid, determine a sum of the input frequency data of theparticular column of the extrapolation rectangle weighted by acorresponding column of the column-wise extrapolation matrix; and whenat least a second low fidelity pixel is to the left or to the right of aparticular row of the extrapolation rectangle in the frequency grid,determine a sum of the input frequency data of the particular row of theextrapolation rectangle weighted by a corresponding row of the row-wiseextrapolation matrix.

In Example 7, based on the subject matter of one or any combination ofExamples 1-6, the processing circuitry may be further configured todetermine a group of extrapolation rectangles within the high fidelityregions. A size of the extrapolation rectangles may be equal to a sizeof the basis rectangles. The processing circuitry may be furtherconfigured to, for each extrapolation rectangle, extrapolate the inputfrequency data of the extrapolation rectangle in one or more candidatedirections with respect to the extrapolation rectangle. The candidatedirections may be from a group that includes above, below, to the left,and to the right. The processing circuitry may be further configured to,for each extrapolation rectangle, for a pixel in which extrapolation inmultiple candidate directions is performed, replace the input frequencydata of the pixel with a value based on a weighted sum of extrapolatedvalues from the multiple extrapolations.

In Example 8, based on the subject matter of one or any combination ofExamples 1-7, weights used for the weighted sum may be based at leastpartly on distances between the pixels in which the extrapolation isperformed and the extrapolation rectangles from which the pixels areextrapolated.

In Example 9, based on the subject matter of one or any combination ofExamples 1-8, the group of extrapolation rectangles may be equivalent tothe group of basis rectangles.

In Example 10, based on the subject matter of one or any combination ofExamples 1-9, the columns of the column-wise extrapolation matrix andthe columns of the basis rectangles may be mapped to a group ofsuccessive column indexes. The rows of the row-wise extrapolation matrixand the rows of the basis rectangles may be mapped to a group ofsuccessive row indexes. For each column index, the column of thecolumn-wise extrapolation matrix mapped to the column index may includea complex set of weights determined in accordance with a forward errorcriterion and a backward error criterion for the input frequency datamapped to columns of the basis rectangles for that are mapped to thecolumn index. For each row index, the row of the row-wise extrapolationmatrix mapped to the row index may include a complex set of weightsdetermined in accordance with a forward error criterion and a backwarderror criterion for the input frequency data mapped to rows of the basisrectangles that are mapped to the row index.

In Example 11, based on the subject matter of one or any combination ofExamples 1-10, the fidelity measurements of the input frequency data mayinclude amplitude measurements of the input frequency data. The regionsmay be classified as high fidelity or low fidelity based at least partlyon comparisons of the amplitude measurements with a predeterminedamplitude threshold.

In Example 12, based on the subject matter of one or any combination ofExamples 1-11, the processing circuitry may be further configured togenerate, for usage in the determination of the parameter of thephysical environment, an output compressed image based on an inverseFourier transform of the output frequency data.

In Example 13, based on the subject matter of one or any combination ofExamples 1-12, the input frequency data may be mapped to the frequencygrid in a dispersed Fourier format that is based on a two-dimensionalFourier transform of two-dimensional compressed image data from thesensor. Each column of the compressed image data may be based on areturn signal from one of the pulsed transmissions of the sensor.

In Example 14, based on the subject matter of one or any combination ofExamples 1-13, the frequency data extrapolator may be included in aradar device that includes the coherently pulsed sensor, and the returnsignals include radar returns.

In Example 15, a method of two-dimensional frequency data extrapolationmay comprise receiving, from a coherently pulsed sensor, input frequencydata mapped to pixels of a two-dimensional frequency grid. The methodmay further comprise dividing, based on fidelity measurements of theinput frequency data, the frequency grid into a group of one or more lowfidelity regions and a group of high fidelity regions. The regions mayinclude contiguous groups of the pixels. The method may further comprisedividing the high fidelity regions to include a group of non-overlappingbasis rectangles of a same basis rectangle size. The method may furthercomprise determining columns for a column-wise extrapolation matrixbased on correlations between the input frequency data of correspondingcolumns of the basis rectangles and determining rows for a row-wiseextrapolation matrix based on correlations between the input frequencydata of rows of the basis rectangles. The method may further compriseextrapolating, in accordance with the extrapolation matrixes, the inputfrequency data of at least a portion of the pixels of the high fidelityregion to replace the input frequency data of at least a portion of thepixels in the low fidelity regions.

In Example 16, based on the subject matter of Example 15, the method mayfurther comprise generating multiple candidate groups of non-overlappingbasis rectangles. The method may further comprise selecting a firstportion of the candidate groups for which a total area covered by thebasis rectangles of the candidate groups is greater than a predeterminedcoverage threshold. The method may further comprise selecting the groupof basis rectangles as a candidate group from the first portion with amaximum basis rectangle area. A same rectangle size may be used forbasis rectangles of each candidate group, different rectangle sizes maybe used for at least a portion of the candidate groups, locations of thebasis rectangles may be varied between the candidate groups, and numbersof basis rectangles per candidate group may be varied between thecandidate groups.

In Example 17, based on the subject matter of one or any combination ofExamples 15-16, the method may further comprise determining anextrapolation rectangle that is of a same size as the basis rectanglesand is located within the high fidelity regions. The method may furthercomprise extrapolating the input frequency data of the pixels of theextrapolation rectangle into a group of rows of pixels immediately aboveor below the extrapolation rectangle. Extrapolated values for columns ofa first row that is closest to the extrapolation rectangle may be basedon a column-wise sum of the input frequency data of the extrapolationrectangle weighted by corresponding columns of the column-wiseextrapolation matrix. Extrapolated values for columns of subsequent rowsmay be based on column-wise sums, weighted by corresponding columns ofthe column-wise extrapolation matrix, of matrixes formed by shifting outthe input frequency data of the extrapolation rectangle and shifting inextrapolated values of previous rows.

In Example 18, based on the subject matter of one or any combination ofExamples 15-17, the method may further comprise extrapolating the inputfrequency data of the pixels of the extrapolation rectangle into a groupof columns of pixels immediately to the left or right of theextrapolation rectangle. Extrapolated values for rows of a first columnthat is closest to the extrapolation rectangle may be based on arow-wise sum of the input frequency data of the extrapolation rectangleweighted by corresponding rows of the row-wise extrapolation matrix.Extrapolated values for rows of subsequent columns may be based onrow-wise sums, weighted by corresponding rows of the row-wiseextrapolation matrix, of matrixes formed by shifting out the inputfrequency data of the extrapolation rectangle and shifting inextrapolated values of previous columns.

In Example 19, based on the subject matter of one or any combination ofExamples 15-18, the method may further comprise replacing the inputfrequency data of pixels in the low fidelity regions with theextrapolated frequency data of corresponding pixels. The method mayfurther comprise refraining from replacing the input frequency data ofpixels in the high fidelity regions with the extrapolated frequency dataof corresponding pixels.

In Example 20, based on the subject matter of one or any combination ofExamples 15-19, the method may further comprise generating outputfrequency data based on the input frequency data of the high fidelityregions and further based on the extrapolated frequency data of the lowfidelity regions. The input frequency data may be based on returnsignals received at the sensor in response to pulsed transmissions ofthe sensor in a physical environment. The output frequency data may begenerated for usage in a determination of a parameter of the physicalenvironment.

In Example 21, a device may comprise a coherently pulsed sensor. Thesensor may be configured to transmit pulses during transmission periods.The sensor may be further configured to determine, for usage byprocessing circuitry, input frequency data for a frequency grid based onreturn signals received during collection windows for the transmissionperiods. The device may further comprise the processing circuitry. Theprocessing circuitry may be configured to determine a group of basisrectangles within a group of high fidelity regions of the frequencygrid. The processing circuitry may be further configured to determine,for a two-dimensional extrapolation of the input frequency data of thehigh fidelity regions to replace the input frequency data of a group oflow fidelity regions of the frequency grid, a column-wise extrapolationmatrix and a row-wise extrapolation matrix. Columns of the column-wiseextrapolation matrix may be determined per column based on the inputfrequency data of corresponding columns of the basis rectangles. Rows ofthe row-wise extrapolation matrix may be determined per row based on theinput frequency data of corresponding rows of the basis rectangles.

In Example 22, based on the subject matter of Example 21, the group ofbasis rectangles may be restricted to a group of non-overlappingrectangles of a same basis rectangle size. The group of basis rectanglesmay be determined in accordance with a joint maximization of a basisrectangle area and a portion of the high fidelity regions covered by thebasis rectangles.

In Example 23, based on the subject matter of one or any combination ofExamples 21-22, the processing circuitry may be further configured todetermine an extrapolation rectangle within the high fidelity regions.The processing circuitry may be further configured to, as part of anextrapolation of the input frequency data of the extrapolation rectangleto replace the input frequency data of a group of low fidelity pixels ofthe low fidelity regions: when at least a first low fidelity pixel isabove or below a particular column of the extrapolation rectangle in thefrequency grid, determine a sum of the input frequency data of theparticular column of the extrapolation rectangle weighted by acorresponding column of the column-wise extrapolation matrix; and whenat least a second low fidelity pixel is to the left or to the right of aparticular row of the extrapolation rectangle in the frequency grid,determine a sum of the input frequency data of the particular row of theextrapolation rectangle weighted by a corresponding row of the row-wiseextrapolation matrix.

In Example 24, based on the subject matter of one or any combination ofExamples 21-23, the device may be a radar device. The transmitted pulsesand the return signals may be electromagnetic signals. The processingcircuitry may be further configured to determine an output compressedimage based on an inverse Fourier transform on extrapolated frequencydata for the frequency grid. The processing circuitry may be furtherconfigured to determine, based at least partly on the output compressedimage, a physical characteristic of an object in a physical environmentinto which the pulses are transmitted. The extrapolated frequency datamay include the input frequency data of the high fidelity regions andfurther includes replaced frequency data for the low fidelity regions.

In Example 25, based on the subject matter of one or any combination ofExamples 21-24, the device may be a sonar device. The transmitted pulsesand the return signals may be based on sound waves. The processingcircuitry may be further configured to determine an output compressedimage based on an inverse Fourier transform on extrapolated frequencydata for the frequency grid. The processing circuitry may be furtherconfigured to determine, based at least partly on the output compressedimage, a physical characteristic of an object in a physical environmentinto which the pulses are transmitted. The extrapolated frequency datamay include the input frequency data of the high fidelity regions andfurther includes replaced frequency data for the low fidelity regions.

The Abstract is provided to comply with 37 C.F.R. Section 1.72(b)requiring an abstract that will allow the reader to ascertain the natureand gist of the technical disclosure. It is submitted with theunderstanding that it will not be used to limit or interpret the scopeor meaning of the claims. The following claims are hereby incorporatedinto the detailed description, with each claim standing on its own as aseparate embodiment.

What is claimed is:
 1. A frequency data extrapolator, comprising:memory; and processing circuitry, configured to: receive input frequencydata mapped to a two-dimensional frequency grid, the input frequencydata based on return signals received at a sensor in response to pulsedtransmissions of the sensor in a physical environment; classify regionsof the frequency grid as high fidelity or low fidelity based at leastpartly on fidelity measurements of the input frequency data: determine agroup of basis rectangles within the high fidelity regions; determine acolumn-wise extrapolation matrix and a row-wise extrapolation matrixbased on the input frequency data of the basis rectangles; generate atwo-dimensional extrapolation of the input frequency data of the highfidelity regions to replace the input frequency data of the low fidelityregions, based on the column-wise extrapolation matrix and the row-wiseextrapolation matrix; and generate output frequency data for usage indetermination of a parameter of the physical environment, based on thetwo-dimensional extrapolation.
 2. The frequency data extrapolatoraccording to claim 1, wherein: columns of the column-wise extrapolationmatrix are determined per column based on the input frequency data ofcorresponding columns of the basis rectangles, and rows of the row-wiseextrapolation matrix are determined per row based on the input frequencydata of corresponding rows of the basis rectangles.
 3. The frequencydata extrapolator according to claim 1, wherein: the group of basisrectangles is restricted to a group of non-overlapping rectangles of asame basis rectangle size, and the group of basis rectangles isdetermined in accordance with a joint maximization of a basis rectanglearea and a portion of the high fidelity regions covered by the basisrectangles.
 4. The frequency data extrapolator according to claim 3, theprocessing circuitry further configured to: generate multiple candidategroups of non-overlapping basis rectangles for which basis rectanglesizes per candidate group are variable; select a first portion of thecandidate groups for which total areas covered by the basis rectanglesof the candidate groups are greater than a predetermined coveragethreshold; and select the group of basis rectangles as a candidate groupfrom the first portion with a maximum basis rectangle area.
 5. Thefrequency data extrapolator according to claim 1, the processingcircuitry further configured to: determine an extrapolation rectanglewithin the high fidelity regions; and as part of an extrapolation of theinput frequency data of the extrapolation rectangle to replace the inputfrequency data of a group of low fidelity pixels of the low fidelityregions: when at least a first low fidelity pixel is above or below aparticular column of the extrapolation rectangle in the frequency grid,determine a sum of the input frequency data of the particular column ofthe extrapolation rectangle weighted by a corresponding column of thecolumn-wise extrapolation matrix, and when at least a second lowfidelity pixel is to the left or to the right of a particular row of theextrapolation rectangle in the frequency grid, determine a sum of theinput frequency data of the particular row of the extrapolationrectangle weighted by a corresponding row of the row-wise extrapolationmatrix.
 6. The frequency data extrapolator according to claim 1, theprocessing circuitry further configured to: determine a group ofextrapolation rectangles within the high fidelity regions, wherein asize of the extrapolation rectangles is equal to a size of the basisrectangles; for each extrapolation rectangle: extrapolate the inputfrequency data of the extrapolation rectangle in one or more candidatedirections with respect to the extrapolation rectangle, the candidatedirections from a group that includes above, below, to the left, and tothe right; for a pixel in which extrapolation in multiple candidatedirections is performed, replace the input frequency data of the pixelwith a value based on a weighted sum of extrapolated values from themultiple extrapolations.
 7. The frequency data extrapolator according toclaim 6, wherein weights used for the weighted sum are based at leastpartly on distances between the pixels in which the extrapolation isperformed and the extrapolation rectangles from which the pixels areextrapolated.
 8. The frequency data extrapolator according to claim 6,wherein the group of extrapolation rectangles is equivalent to the groupof basis rectangles.
 9. The frequency data extrapolator according toclaim 1, wherein: columns of the column-wise extrapolation matrix andcolumns of the basis rectangles are mapped to a group of successivecolumn indexes, rows of the row-wise extrapolation matrix and rows ofthe basis rectangles are mapped to a group of successive row indexes,for each column index: the column of the column-wise extrapolationmatrix mapped to the column index includes a complex set of weightsdetermined in accordance with a forward error criterion and a backwarderror criterion for the input frequency data mapped to columns of thebasis rectangles for that are mapped to the column index, for each rowindex: the row of the row-wise extrapolation matrix mapped to the rowindex includes a complex set of weights determined in accordance with aforward error criterion and a backward error criterion for the inputfrequency data mapped to rows of the basis rectangles that are mapped tothe row index.
 10. The frequency data extrapolator according to claim 1,wherein: the fidelity measurements of the input frequency data includeamplitude measurements of the input frequency data, and the regions areclassified as high fidelity or low fidelity based at least partly oncomparisons of the amplitude measurements with a predetermined amplitudethreshold.
 11. The frequency data extrapolator according to claim 1, theprocessing circuitry further configured to: generate, for usage in thedetermination of the parameter of the physical environment, an outputcompressed image based on an inverse Fourier transform of the outputfrequency data.
 12. The frequency data extrapolator according to claim1, wherein: the input frequency data is mapped to the frequency grid ina dispersed Fourier format that is based on a two-dimensional Fouriertransform of two-dimensional compressed image data from the sensor, andeach column of the compressed image data is based on a return signalfrom one of the pulsed transmissions of the sensor.
 13. A method oftwo-dimensional frequency data extrapolation, the method comprising:receiving, from a coherently pulsed sensor, input frequency data mappedto pixels of a two-dimensional frequency grid: dividing, based onfidelity measurements of the input frequency data, the frequency gridinto a group of one or more low fidelity regions and a group of highfidelity regions, wherein the regions include contiguous groups of thepixels; dividing the high fidelity regions to include a group ofnon-overlapping basis rectangles of a same basis rectangle size;determining columns for a column-wise extrapolation matrix based oncorrelations between the input frequency data of corresponding columnsof the basis rectangles and determining rows for a row-wiseextrapolation matrix based on correlations between the input frequencydata of rows of the basis rectangles; and extrapolating, in accordancewith the extrapolation matrixes, the input frequency data of at least aportion of the pixels of the high fidelity region to replace the inputfrequency data of at least a portion of the pixels in the low fidelityregions.
 14. The method according to claim 13, the method furthercomprising: generating multiple candidate groups of non-overlappingbasis rectangles, selecting a first portion of the candidate groups forwhich a total area covered by the basis rectangles of the candidategroups is greater than a predetermined coverage threshold; and selectingthe group of basis rectangles as a candidate group from the firstportion with a maximum basis rectangle area, wherein a same rectanglesize is used for basis rectangles of each candidate group, differentrectangle sizes are used for at least a portion of the candidate groups,locations of the basis rectangles are varied between the candidategroups, and numbers of basis rectangles per candidate group is variedbetween the candidate groups.
 15. The method according to claim 13, themethod further comprising: determining an extrapolation rectangle thatis of a same size as the basis rectangles and is located within the highfidelity regions; and extrapolating the input frequency data of thepixels of the extrapolation rectangle into a group of rows of pixelsimmediately above or below the extrapolation rectangle, whereinextrapolated values for columns of a first row that is closest to theextrapolation rectangle is based on a column-wise sum of the inputfrequency data of the extrapolation rectangle weighted by correspondingcolumns of the column-wise extrapolation matrix, and whereinextrapolated values for columns of subsequent rows are based oncolumn-wise sums, weighted by corresponding columns of the column-wiseextrapolation matrix, of matrixes formed by shifting out the inputfrequency data of the extrapolation rectangle and shifting inextrapolated values of previous rows.
 16. The method according to claim15, the method further comprising: extrapolating the input frequencydata of the pixels of the extrapolation rectangle into a group ofcolumns of pixels immediately to the left or right of the extrapolationrectangle, wherein extrapolated values for rows of a first column thatis closest to the extrapolation rectangle is based on a row-wise sum ofthe input frequency data of the extrapolation rectangle weighted bycorresponding rows of the row-wise extrapolation matrix, and whereinextrapolated values for rows of subsequent columns are based on row-wisesums, weighted by corresponding rows of the row-wise extrapolationmatrix, of matrixes formed by shifting out the input frequency data ofthe extrapolation rectangle and shifting in extrapolated values ofprevious columns.
 17. The method according to claim 13, the methodfurther comprising: replacing the input frequency data of pixels in thelow fidelity regions with the extrapolated frequency data ofcorresponding pixels; and refraining from replacing the input frequencydata of pixels in the high fidelity regions with the extrapolatedfrequency data of corresponding pixels.
 18. The method according toclaim 13, the method further comprising: generating output frequencydata based on the input frequency data of the high fidelity regions andfurther based on the extrapolated frequency data of the low fidelityregions, wherein the input frequency data is based on return signalsreceived at the sensor in response to pulsed transmissions of the sensorin a physical environment, and wherein the output frequency data isgenerated for usage in a determination of a parameter of the physicalenvironment.
 19. A device, comprising: a coherently pulsed sensor,configured to: transmit pulses during transmission periods; anddetermine, for usage by processing circuitry, input frequency data for afrequency grid based on return signals received during collectionwindows for the transmission periods, and the processing circuitry,configured to: determine a group of basis rectangles within a group ofhigh fidelity regions of the frequency grid; determine, for atwo-dimensional extrapolation of the input frequency data of the highfidelity regions to replace the input frequency data of a group of lowfidelity regions of the frequency grid, a column-wise extrapolationmatrix and a row-wise extrapolation matrix, wherein columns of thecolumn-wise extrapolation matrix are determined per column based on theinput frequency data of corresponding columns of the basis rectangles,and wherein rows of the row-wise extrapolation matrix are determined perrow based on the input frequency data of corresponding rows of the basisrectangles.
 20. The device according to claim 19, wherein: the group ofbasis rectangles is restricted to a group of non-overlapping rectanglesof a same basis rectangle size, and the group of basis rectangles isdetermined in accordance with a joint maximization of a basis rectanglearea and a portion of the high fidelity regions covered by the basisrectangles.
 21. The device according to claim 19, the processingcircuitry further configured to: determine an extrapolation rectanglewithin the high fidelity regions; and as part of an extrapolation of theinput frequency data of the extrapolation rectangle to replace the inputfrequency data of a group of low fidelity pixels of the low fidelityregions: when at least a first low fidelity pixel is above or below aparticular column of the extrapolation rectangle in the frequency grid,determine a sum of the input frequency data of the particular column ofthe extrapolation rectangle weighted by a corresponding column of thecolumn-wise extrapolation matrix, and when at least a second lowfidelity pixel is to the left or to the right of a particular row of theextrapolation rectangle in the frequency grid, determine a sum of theinput frequency data of the particular row of the extrapolationrectangle weighted by a corresponding row of the row-wise extrapolationmatrix.
 22. The device according to claim 19, wherein: the device is aradar device, the transmitted pulses and the return signals areelectromagnetic signals, the processing circuitry is further configuredto: determine an output compressed image based on an inverse Fouriertransform on extrapolated frequency data for the frequency grid; anddetermine, based at least partly on the output compressed image, aphysical characteristic of an object in a physical environment intowhich the pulses are transmitted, wherein the extrapolated frequencydata includes the input frequency data of the high fidelity regions andfurther includes replaced frequency data for the low fidelity regions.23. The device according to claim 19, wherein: the device is a sonardevice, the transmitted pulses and the return signals are based on soundwaves, the processing circuitry is further configured to: determine anoutput compressed image based on an inverse Fourier transform onextrapolated frequency data for the frequency grid; and determine, basedat least partly on the output compressed image, a physicalcharacteristic of an object in a physical environment into which thepulses are transmitted, wherein the extrapolated frequency data includesthe input frequency data of the high fidelity regions and furtherincludes replaced frequency data for the low fidelity regions.